The influenza surveillance has been received much attention in public health area. For the cases with excessive zeroes, the zero-inflated Poisson process is widely used. However, the traditional control charts based on zero-inflated Poisson model, ignore the association between influenza cases and risk factors, and thus may lead to unexpected mistakes when implementing monitoring charts. In this paper, we proposed risk-adjusted zero-inflated Poisson cumulative sum control charts, in which the risk factors were put to adjust the risk of influenza and the adjustment was made by zero-inflated Poisson regression. We respectively proposed the control chart monitoring the parameters individually and simultaneously. The performance of our proposed risk-adjusted zero-inflated Poisson cumulative sum control chart was evaluated and compared with the unadjusted standard cumulative sum control charts in simulation studies. The results show that for different distribution of impact factors and different coefficients, the risk-adjusted cumulative sum charts can generate much less false alarm than the standard ones. Finally, the influenza surveillance data from Hong Kong is used to illustrate the application of the proposed chart. Our results suggest that the adjusted cumulative sum control chart we proposed is more accurate and credible than the unadjusted standard control charts because of the lower false alarm rate of the adjusted ones. Even the unadjusted control charts may signal a little faster than the adjusted ones, the alarm they raise may have low credibility since they also raise alarm frequently even the processes are in control. Thus we suggest using the risk-adjusted cumulative sum control charts to monitor the influenza surveillance data to alert accurately, credibly and relatively quickly.
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